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Why Is the magnitude of instantaneous velocity always equal to the instantaneous speed?
Yes, it can be. Average speed is the distance traveled divided by the time traveled. Average velocity is the displacement divided by the time traveled. Displacement is change in position, or final position (df) minus initial position (di).
Let's say you traveled from your home to the mall and then back again. The total distance traveled was 30 miles, and the total time driven was 1 hour.
Average speed = distance traveled/time traveled = 30 miles/1 hour = 30mi/hr or 30mph.
Average velocity = (df - di)/time traveled = 0 mile/1 hour = 0 mi/hr or 0mph.*
*In this case the final position and the initial position are the same (your house), so the displacement is zero.
Something to think about: When a Nascar driver races 500 miles around an oval track, his average speed might be 160mph, but his average velocity when he finishes the race is 0mph.
What else can I help you with?
When is the average velocity is equal to the instantaneous velocity?
Average velocity equals the average speed if (and only if) the motion is in the same direction. If not, the average speed, being the average of the absolute value of the velocity, will be larger.
When is the instantaneous velocity equal to avg velocity?
Mainly, when the velocity doesn't change. Also, in the case of varying velocity, the instantaneous velocity might, for a brief instant, be equal to the average velocity.
Does the instantaneous speed ever equal the magnitude of its average velocity?
Yes. For a start, this happens when the object moves at a constant velocity. Also, if moving in a straight line, even if the object changes speed there must needs be a moment when its instantaneous speed is equal to its average speed - since it cannot change speed suddenly, it must do so gradually.
Instantaneous speed at an instant is equal to magnitude of instantaneous velocity at that instant?
That's correct, the instantaneous magnitudes are equal. Non-instantaneous values may not be equal. For example, to find average speed, between two points, you divide the actual path distance by the time, but for average velocity you divide the straight line distance, between the points, by the time. The straight line distance could be quite a bit shorter then the actual path distance (for curved motion) so you could get a big difference between those averages. When calculating "instantaneous" values, however, the difference between "actual path distance" and "straight line distance" becomes insignificant, because you are using distances for infintesimally small time intervals.
When is an object's average velocity equal to its instantaneous velocity?
An object's average velocity is equal to its instantaneous velocity when the object is moving at a constant speed in a straight line. This means that the object covers equal distances in equal intervals of time, resulting in the average velocity over a period of time being equal to the instantaneous velocity at any given moment within that period.
Is the magnitude of instantaneous velocity always equal to the instantaneous speed?
Because speed is the magnitude of the velocity vector. The velocity consists of the speed and the direction, and the whole thing can be embodied in a 3D vector. If you like the velocity is the magnitude (the speed), which is a scalar (just a real number), multiplied by a unit vector in the right direction.
When is speed equal to the magnitude of velocity?
Speed is equal to the magnitude of velocity when the object is moving in a straight line without changing direction. In other words, if the velocity vector is pointing in the same direction as the motion of the object, then the speed will be equal to the magnitude of the velocity.
When is the average velocity is equal to the instantaneous velocity?
Average velocity equals the average speed if (and only if) the motion is in the same direction. If not, the average speed, being the average of the absolute value of the velocity, will be larger.
When is the instantaneous velocity equal to avg velocity?
Mainly, when the velocity doesn't change. Also, in the case of varying velocity, the instantaneous velocity might, for a brief instant, be equal to the average velocity.
Does the instantaneous speed ever equal the magnitude of its average velocity?
Yes. For a start, this happens when the object moves at a constant velocity. Also, if moving in a straight line, even if the object changes speed there must needs be a moment when its instantaneous speed is equal to its average speed - since it cannot change speed suddenly, it must do so gradually.
Instantaneous speed at an instant is equal to magnitude of instantaneous velocity at that instant?
That's correct, the instantaneous magnitudes are equal. Non-instantaneous values may not be equal. For example, to find average speed, between two points, you divide the actual path distance by the time, but for average velocity you divide the straight line distance, between the points, by the time. The straight line distance could be quite a bit shorter then the actual path distance (for curved motion) so you could get a big difference between those averages. When calculating "instantaneous" values, however, the difference between "actual path distance" and "straight line distance" becomes insignificant, because you are using distances for infintesimally small time intervals.
When will the average velocity be equal to instantaneous velocity?
In uniform motion.
When is speed equal to magnitude of velocity?
Speed is equal to the magnitude of velocity almost always. Speed is total distance / total time no matter which way the distance goes. Velocity is the distance from a starting point divided by total time.
When average velocity is equal to its instantaneous velocity acceleration?
you are still. motion is at rest.
When average velocity and average speed is equal?
For the instantaneous value of average velocity, average speed and average velocity are equal.
Instantaneous speed at an instant is equal to magnitude of instantaneous velocity at that instant Why is it so?
Instantaneous velocity mean change of displacement in extremely small amount time. (in math way, taking[ lim t--->0 (change in displacements/change in time) ]. instantaneous speed is the same expect displacement change to distance. So,because of very very small change in time, magnitude of distance and displacement will be same for any direction the object is moving.
When is an object's average velocity equal to its instantaneous velocity?
An object's average velocity is equal to its instantaneous velocity when the object is moving at a constant speed in a straight line. This means that the object covers equal distances in equal intervals of time, resulting in the average velocity over a period of time being equal to the instantaneous velocity at any given moment within that period.
